If f of x is equal to the fraction with numerator x minus 3 and denominator x , g of x is equal to x plus 3 , and h of x is equal to 2 x plus 1 , what is open paren g circ h circ f close paren times x ?
Answer
A
open paren g circ h circ f close paren times x is equal to the fraction with numerator 8 x plus 1 and denominator 2 x plus 1
B
open paren g circ h circ f close paren times x is equal to the fraction with numerator 3 x minus 6 and denominator x
C
open paren g circ h circ f close paren times x is equal to the fraction with numerator 2 x plus 4 and denominator 2 x plus 7
D
open paren g circ h circ f close paren times x is equal to the fraction with numerator 6 x minus 6 and denominator x
Explanation
Apply the functions from right to left. First, f(x) = (x − 3)/x. Then h(f(x)) = 2(x − 3)/x + 1 = (3x − 6)/x. Finally, g adds 3, giving (g ∘ h ∘ f)(x) = (3x − 6)/x + 3 = (6x − 6)/x, which is choice D.
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